Data from: Multiple scaling behavior and nonlinear traits in music scores

We present a statistical analysis of music scores from different composers using detrended fluctuation analysis. We find different fluctuation profiles that correspond to distinct auto-correlation structures of the musical pieces. Further, we reveal evidence for the presence of nonlinear auto-correlations by estimating the detrended fluctuation analysis of the magnitude series, a result validated by a corresponding study of appropriate surrogate data. The amount and the character of nonlinear correlations vary from one composer to another. Finally, we performed a simple experiment in order to evaluate the pleasantness of the musical surrogate pieces in comparison with the original music and find that nonlinear correlations could play an important role in the aesthetic perception of a musical piece.本研究采用去趋势波动分析（Detrended Fluctuation Analysis）对不同作曲家的乐谱展开统计分析。结果显示，不同乐曲呈现出各异的波动特征，这些特征对应着乐曲独特的自相关结构。进一步地，我们通过对幅度序列执行去趋势波动分析，揭示了非线性自相关存在的相关证据；该结论通过针对合适替代数据的对应研究得到了验证。不同作曲家的非线性相关关系的数量与特征均存在显著差异。最后，我们设计了一项简易对照实验，对音乐替代片段与原始乐曲的悦耳程度进行评估，结果发现非线性相关关系可能对乐曲的审美感知起到重要作用。